### Problem Statement

The product value of a string is the product of all the digits ('0'-'9') in the string. For example, the product value of "123" is 1 * 2 * 3 = 6.

A string is called colorful if it contains only digits and the product value of each of its nonempty contiguous substrings is distinct.

For example, the string "263" has six substrings: "2", "6", "3", "26", "63" and "263". The product values of these substrings are: 2, 6, 3, 2 * 6 = 12, 6 * 3 = 18 and 2 * 6 * 3 = 36, respectively. Since all six product values are distinct, "263" is colorful.

On the other hand, "236" is not colorful because two of its substrings, "6" and "23", have the same product value (6 = 2 * 3).

Return the k-th (1-based) lexicographically smallest colorful string of length n. If there are less than k colorful strings of length n, return an empty String instead.

### Definition

 Class: ColorfulStrings Method: getKth Parameters: int, int Returns: String Method signature: String getKth(int n, int k) (be sure your method is public)

### Notes

-The lexicographically smaller of two strings is the one that has the smaller character ('0' < '1' < ... < '9') at the first position where they differ.

### Constraints

-n will be between 1 and 50, inclusive.
-k will be between 1 and 1,000,000,000, inclusive.

### Examples

0)

 `3` `4`
`Returns: "238"`
 The first four smallest colorful strings of length 3 are "234", "235", "237" and "238".
1)

 `4` `2000`
`Returns: ""`
 The number of colorful strings of length 4 is less than 2000.
2)

 `5` `1`
`Returns: "23457"`
3)

 `2` `22`
`Returns: "52"`
4)

 `6` `464`
`Returns: "257936"`

#### Problem url:

http://www.topcoder.com/stat?c=problem_statement&pm=10724

#### Problem stats url:

http://www.topcoder.com/tc?module=ProblemDetail&rd=14149&pm=10724

lyrically

#### Testers:

PabloGilberto , ivan_metelsky , it4.kp

#### Problem categories:

Brute Force, Search